ECT sensors can cause rough idle -messes with the air fuel ratio.
It’s probably idling rough after warm-up because that is when the car goes into closed-loop fuel control, adjusting the fuel supply based on feedback from the o2 sensors and other sensors involved in the fuel control system. On cold start, it is operating off the fuel table and ignoring the sensor readings.
But, yes, that seems to point away from things like piston slap or crankshaft issues, and towards something in the fuel/air control or supply systems. Is that supercharger still making clunking noises?
Again,if neither you nor your mechanic have a way to read the codes or the real-time parameters, you are likely to spend more money in guesswork replacement parts than you would by just buying the GAP tool and replacing the parts that a subsequent diagnosis might recommend.
In spite of how helpful people are on this forum, I’m not sure how much more help you can get from it without some data to point us to. To me it feels as though you are asking us if a part might cause shaky idle when warmed up, and the answer is probably “yes”, not because it is likely that part but more because there are a lot of different parts that might cause a shaky idle.
If your sc is not outputting the expected boost, that might be messing up your idle as well. Not to mention that particles of metal might be going into your cylinders if the sc blades really are contacting each other. I find it hard to imagine slop in the blade shafts is really the problem.
When does the sc make the clunking noise? all the time? just at startup or shut down, or when hitting the gas hard or releasing throttle?
If it sounds something like marbles rattling, that’s just the isolator/coupler. Known issue and easy fix, but won’t affect performance.
Otherwise, I still wonder if it might be the bypass valve. If there is something wrong with the bypass, I think it will affect performance.